Question

5. In a trapezium ABCD, AB || DC, AB = 30 cm, BC
= 15 cm, DC = 44 cm and AD = 13 cm. Find the
area of the trapezium.
​

Answer 1

$\huge \dag \:{ \underline{ \boxed{ \purple{ \mathfrak{Answer}}}}}$

Area of trapezium = 444  cm²

Step-by-step explanation:

AB = 30 cm

CD = 44

Draw AM ⊥ CD  & BN ⊥CD

AM = BN = y

MN = 30 cm

DM = x cm

=> CN = 44 - (30 + x) = 14 - x  cm

AD = 13 cm

AD² = AM² + DM²

=> 13² = y² + x²

BC = 15 cm

=> BC² = BN² + CN²

=> 15² = y²  + (14 - x)²

=> 15² - 13² =  (14 - x)² - x²

=> 28 * 2 = (14) (1 4 - 2x)

=> 4 = 14 - 2x

=> 2x = 10

=> x = 5

13² = y² + x²

=>   13² = y² + 5²

=> y² = 144

=> y = 12

AM = BN = 12 cm

Area of Trapezium = (1/2) (AB + CD) * AM

= (1/2)(30 + 44) * 12

= 6 * 74

= 444  cm²

area of trapezium = 444  cm²